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4 years ago

To convert drams to grams, multiply the number of drams by which number?

1 answer:

5 0

"Dram" is a unit of volume, whereas "gram" is a unit of mass.
They can't be directly converted. If they both refer to a sample
of some substance, then the conversion depends on the density
of the substance. All we can say for sure by way of an answer is:
To change 'drams' to 'grams', replace the 'd' with 'g'.

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Use the substitution u = tan(x) to evaluate the following. int_0^(pi/6) (text(tan) ^2 x text( sec) ^4 x) text( ) dx

Rudiy27

If we use the substitution $u = \tan x$ , then $du = \sec^2 {x}\ dx$ . If you try substituting just $u$ and $du$ into the integrand, though, you'll notice that there's a $\sec^2x$ left over that we have to deal with.

To get rid of this problem, use the identity $\tan^2 x + 1 = \sec^2 x$ and substitute in the left side of the identity for the extra $\sec^2x$ , as shown:

$\int\limits^{\pi/6}_0 {tan^2 x \ sec^4 x} \, dx$
$\int\limits^{\pi/6}_0 {tan^2 x \ (tan^2 x + 1) \ sec^2 x} \, dx$

From there, we can substitute in $u$ and $du$ , and then evaluate:

$\int\limits^{\pi/6}_0 {tan^2 x \ (tan^2 x + 1) \ sec^2 x} \, dx$
$\int\limits^{\frac{1}{\sqrt{3}}}_0 {u^2(u^2 + 1)} \, du$
$\int\limits^{\frac{1}{\sqrt{3}}}_0 {u^4 + u^2} \, du$
$= \left.\frac{u^5}{5} + \frac{u^3}{3}\right|_0^\frac{1}{\sqrt{3}}$
$= (\frac{(\frac{1}{\sqrt{3}})^5}{5} + \frac{(\frac{1}{\sqrt{3}})^3}{3}) - (\frac{(0)^5}{5} + \frac{(0)^3}{3})$
$= \frac{1}{45\sqrt{3}} + \frac{1}{9\sqrt{3}} = \frac{6}{45\sqrt{3}} = \bf \frac{2}{15\sqrt{3}}$

8 0

3 years ago

In physics, it is important to use mathematical approximations. for instance, in a small angle approximation, tanα ∼ sin α . fin

siniylev [52]

Note that x is measured in radians.
The percent difference or error between sin(x) and tan(x) is calculated as
$d = 100( \frac{|sin(x)-tan(x)|}{sin(x)} )$

We want this percent difference to be less than 10.4%.
Because tan(x) > sin(x) for small values of x, define
$f(x) = \frac{tan(x)-sin(x)}{sin(x)}= 0.104 \\ or \\ sec(x) - 1 = 0.104 \\ sec(x) = 1.104$

From the calculator, obtain
sec⁻¹ 1.104 = 0.4375

Answer: x = 0.4375 radians

5 0

3 years ago

Function f and function g are inverses of one another. What is f(g(t)) equal to?

a_sh-v [17]

Hello from MrBillDoesMath!

Answer: f(g(t)) = t

Discussion:

A function and its inverse "undo" each other. Suppose that

f(t) = t^2 and g(t) = t^ (1/2)

Then

A B C

g(f(t)) = g (t^2) = (t^2) ^ (1/2) = t

A: substitute the definition of f(t), that is t^2, in the equation

B: g(t) takes the square root if its argument

C: The square root of a squared item is the item itself.

Regards, MrB

3 0

3 years ago

Find the measure of each side of an equilateral triangle whose area is √3 cm<br>STEP BY STEP

Dafna11 [192]

Answer:

s = 2 cm

Step-by-step explanation:

Given the following data;

Area of equilateral triangle = √3 cm

Mathematically, the area of an equilateral triangle is given by the formula;

A = √3 * s²/4

Where, s represents the sides of length.

Substituting into the formula, we have;

√3 = √3 * s²/4

Dividing both sides by √3, we have;

1 = s²/4

Cross-multiplying, we have;

4 = s²

Taking the square root of both sides, we have;

s = √4

s = 2 cm

3 0

3 years ago

NEED HELP WITH THIS PLEASE DUE TODAY the third picture its together with the second one

kogti [31]

Answer:

-3

-2.5

-2

-9/8

-1

-1/4

1/4

9/8

8/3

2.5

6 0

3 years ago